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Despite observational evidences, InfraRed (IR) excess of classical Cepheidsare seldom studied and poorly understood, but probably induces systematics onthe Period-Luminosity (PL) relation used in the calibration of theextragalactic distance scale. This study aims to understand the physical originof the IR excess found in the spectral energy distribution (SED) of 5 Cepheids: RS Pup (P=41.46d), zeta Gem (P=10.15d), eta Aql (P=7.18d), V Cen (P=5.49d)and SU Cyg (P=3.85d). A time series of atmospheric models along the pulsationcycle are fitted to a compilation of data, including optical and near-IRphotometry, Spitzer spectra (secured at a specific phase), interferometricangular diameters, effective temperature and radial velocity measurements.Herschel images in two bands are also analyzed qualitatively. In this fittingprocess, based on the SPIPS algorithm, a residual is found in the SED, whateverthe pulsation phase, and for wavelengths larger than about $1.2\mu$m, whichcorresponds to the so-determined infrared excess of Cepheids. This IR excess isthen corrected from interstellar medium absorption in order to infer or not thepresence of dust shells, and is finally used in order to fit a model of a shellof ionized gas. For all Cepheids, we find a continuum IR excess increasing upto about -0.1 magnitudes at 30$\mu$m, which cannot be explained by a hot orcold dust model of CircumStellar Environment (CSE). We show, for the firsttime, that the IR excess of Cepheids can be explained by free-free emissionfrom a thin shell of ionized gas, with a thickness of about 15% of the starradius, a mass of $10^{-9}-10^{-7}$ Msol and a temperature ranging from 3500 to4500K. This result has to be tested with interferometers operating in visible,in the mid-IR or in the radio domain. The impact of such CSEs of ionized gas onthe PL relation of Cepheids needs also more investigations.

A thin shell of ionized gas explaining the IR excess of classical Cepheids